Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4664053 | Acta Mathematica Scientia | 2012 | 11 Pages |
Abstract
Let L = −ΔHn + V be a Schrödinger operator on Heisenberg group Hn, where ΔHn is the sublaplacian and the nonnegative potential V belongs to the reverse Hölder class BQ/2, where Q is the homogeneous dimension of Hn. Let T1=(−ΔHn+V)−1V,T2=(−ΔHn+V)−1/2V1/2, and T3=(−ΔHn+V)−1/2∇Hn, then we verify that [b, Ti], i = 1,2,3 are bounded on some Lp(Hn), where b ∈ BMO(Hn). Note that the kernel of Ti, i = 1,2,3 has no smoothness.
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